Related papers: Robust and Accurate Cylinder Triangulation
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
This paper proposes a new extrinsic calibration of kaleidoscopic imaging system by estimating normals and distances of the mirrors. The problem to be solved in this paper is a simultaneous estimation of all mirror parameters consistent…
We present an efficient method for joint optimization of topology, materials and lighting from multi-view image observations. Unlike recent multi-view reconstruction approaches, which typically produce entangled 3D representations encoded…
We present an algorithm to estimate the rotation pole of a principal-axis rotator using silhouette images collected from multiple camera poses. First, a set of images is stacked to form a single silhouette-stack image, where the object's…
Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be…
Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this…
Robustness verification is a promising technique for rigorously proving Recurrent Neural Networks (RNNs) robustly. A key challenge is to over-approximate the nonlinear activation functions with linear constraints, which can transform the…
Single image super-resolution (SISR) is a very popular topic nowadays, which has both research value and practical value. In daily life, we crop a large image into sub-images to do super-resolution and then merge them together. Although…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…
In this paper, we study closed-form optimal solutions to two-view triangulation with known internal calibration and pose. By formulating the triangulation problem as $L_1$ and $L_\infty$ minimization of angular reprojection errors, we…
The problem of self-calibration of two cameras from a given fundamental matrix is one of the basic problems in geometric computer vision. Under the assumption of known principal points and square pixels, the well-known Bougnoux formula…
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of…
We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimiser both under the…
The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…